Question

Give an example of a maximal ideal in a noncommutative ring which is not prime

score 2.6k · Answer 1 · 2026-04-12 18:10:40

2.6k

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Give an example of a maximal ideal in a noncommutative ring which is not prime

Published on 12 Apr 2026 - 18:10

score 49 · Answer 2 · 2026-04-16 10:56:15

49

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Prove that $M_{n\times n}(K)$ and $P_{n^2-1}[x]$ are not isomorphic rings

Published on 16 Apr 2026 - 10:56

score 1.4k · Answer 3 · 2026-04-15 00:58:40

1.4k

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Prove that the intersection of all maximal left ideals of a ring $R$ is a two sided ideal

Published on 15 Apr 2026 - 0:58

score 158 · Answer 4 · 2026-04-12 16:25:28

158

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Morphism of $k$-algebras between matrix rings over $k$

Published on 12 Apr 2026 - 16:25

score 373 · Answer 5 · 2026-04-15 22:33:39

373

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The ring Z/pZ[Z/pZ] (p is a prime) is not a semi-simple ring.

Published on 15 Apr 2026 - 22:33

score 257 · Answer 6 · 2026-04-13 05:19:31

257

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What exactly does it mean for a maximal ideal to be unique in a principal ideal domain?

Published on 13 Apr 2026 - 5:19

score 115 · Answer 7 · 2026-04-16 19:44:29

Let R be a finite commutative ring with 1.Let a,b∈ R such that (a)+(b)=R and M be any maximal ideal of R with b∉M. Then is some x∈ R such that a+xb∉M

score 537 · Answer 8 · 2026-04-16 01:04:11

537

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Show some polynomial is irreducible over the field of 7 elements.

Published on 16 Apr 2026 - 1:04

score 1.3k · Answer 9 · 2026-04-27 21:08:56

1.3k

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The krull dimension of $\Bbb{Z}$ and artinian rings

Published on 27 Apr 2026 - 21:08

score 961 · Answer 10 · 2026-04-15 22:00:00

961

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Surjective ring homomorphism from $M_n(R)$ to $M_n(R/I)$ where $R$ is a ring and $I$ is an ideal for R?

Published on 15 Apr 2026 - 22:00

score 717 · Answer 11 · 2026-04-17 16:02:05

717

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Quotient Field of an Integral Domain

Published on 17 Apr 2026 - 16:02

score 47 · Answer 12 · 2026-04-16 14:48:53

47

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Questions related to the concept of $k$-algebras

Published on 16 Apr 2026 - 14:48

score 801 · Answer 13 · 2026-04-12 22:12:09

801

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Sum and product of comaximal ideals

Published on 12 Apr 2026 - 22:12

score 176 · Answer 14 · 2026-04-15 23:17:51

176

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If $\cap_{j=1}^{n}I_{j} \subseteq P$ for any ideals $I_1,I_2,..I_n$, then $I_j \subseteq P$ for some $j$

Published on 15 Apr 2026 - 23:17

score 1.2k · Answer 15 · 2026-04-15 04:01:03

If I define $ I.J=\{ij : i \in I $ & $ j \in J \} $. Then prove that it is not necessrily an ideal, where $I,J$ are ideals in a ring $R$.

List Question

Give an example of a maximal ideal in a noncommutative ring which is not prime

Prove that $M_{n\times n}(K)$ and $P_{n^2-1}[x]$ are not isomorphic rings

Prove that the intersection of all maximal left ideals of a ring $R$ is a two sided ideal

Morphism of $k$-algebras between matrix rings over $k$

The ring Z/pZ[Z/pZ] (p is a prime) is not a semi-simple ring.

What exactly does it mean for a maximal ideal to be unique in a principal ideal domain?

Let R be a finite commutative ring with 1.Let a,b∈ R such that (a)+(b)=R and M be any maximal ideal of R with b∉M. Then is some x∈ R such that a+xb∉M

Show some polynomial is irreducible over the field of 7 elements.

The krull dimension of $\Bbb{Z}$ and artinian rings

Surjective ring homomorphism from $M_n(R)$ to $M_n(R/I)$ where $R$ is a ring and $I$ is an ideal for R?

Quotient Field of an Integral Domain

Questions related to the concept of $k$-algebras

Sum and product of comaximal ideals

If $\cap_{j=1}^{n}I_{j} \subseteq P$ for any ideals $I_1,I_2,..I_n$, then $I_j \subseteq P$ for some $j$

If I define $ I.J=\{ij : i \in I $ & $ j \in J \} $. Then prove that it is not necessrily an ideal, where $I,J$ are ideals in a ring $R$.

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